Least Common Multiple of 31314 and 31321

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

• Least Common Multiple of 31314 and 31321 by Prime method
• Least Common Multiple of 31314 and 31321 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 31314 and 31321. First we will calculate the prime factors of 31314 and 31321.

Prime Factorization of 31314

Prime factors of 31314 are 2, 3, 17,307. Prime factorization of 31314 in exponential form is:

31314 = 2¹×3¹×17¹×307¹

Prime Factorization of 31321

Prime factors of 31321 are 31321. Prime factorization of 31321 in exponential form is:

31321 = 31321¹

Now multiplying the highest exponent prime factors to calculate the LCM of 31314 and 31321.

LCM(31314,31321) = 2¹×3¹×17¹×307¹×31321¹
LCM(31314,31321) = 980785794

Factors of 31314

List of positive integer factors of 31314 that divides 31314 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 307, 614, 921, 1842, 5219, 10438, 15657, 31314

Factors of 31321

List of positive integer factors of 31321 that divides 31321 without a remainder.

1, 31321

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31314 and 31321, than apply into the LCM equation.

GCF(31314,31321) = 1
LCM(31314,31321) = ( 31314 × 31321) / 1
LCM(31314,31321) = 980785794 / 1
LCM(31314,31321) = 980785794

(i) The LCM of 31321 and 31314 is associative

LCM of 31314 and 31321 = LCM of 31321 and 31314

1. What is the LCM of 31314 and 31321?

Answer: LCM of 31314 and 31321 is 980785794.

2. What are the Factors of 31314?

Answer: Factors of 31314 are 1, 2, 3, 6, 17, 34, 51, 102, 307, 614, 921, 1842, 5219, 10438, 15657, 31314. There are 16 integers that are factors of 31314. The greatest factor of 31314 is 31314.

3. What are the Factors of 31321?

Answer: Factors of 31321 are 1, 31321. There are 2 integers that are factors of 31321. The greatest factor of 31321 is 31321.

4. How to Find the LCM of 31314 and 31321?

Answer:

Least Common Multiple of 31314 and 31321 = 980785794

Step 1: Find the prime factorization of 31314

31314 = 2 x 3 x 17 x 307

Step 2: Find the prime factorization of 31321

31321 = 31321

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 980785794 = 2 x 3 x 17 x 307 x 31321

Step 4: Therefore, the least common multiple of 31314 and 31321 is 980785794.